| Título: | Probabilistic representation of fundamental solutions to $\frac{\partial u}{\partial t} = κ_m \frac{\partial^m u}{\partial x^m}$ |
| Autores: |
Orsingher, Enzo; Sapienza University of Rome D'Ovidio, Mirko; Sapienza University of Rome |
| Fecha: | 2012-01-02 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Pseudo-process; higher-order heat equation; Airy functions; Cauchy distribution; stable laws; fractional diffusion equations 60G52; 35C05 |
| Descripción: | For the fundamental solutions of heat-type equations of order $n$ we give a general stochastic representation in terms of damped oscillations with generalized gamma distributed parameters. By composing the pseudo-process $X_m$ related to the higher-order heat-type equation with positively skewed stable r.v.'s $T^j_{1/3}$, $j=1,2, ..., n$ we obtain genuine r.v.'s whose explicit distribution is given for $n=3$ in terms of Cauchy asymmetric laws. We also prove that $X_3(T^1_{1/3}(...(T^n_{(1/3)}(t))...))$ has a stable asymmetric law. |
| Idioma: | Inglés |
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